Definition of "provability" []

• The condition of being provable (noun)

Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License

• "Discussions of the consequences of Gödel's incompleteness theorems sometimes involve confusion around the notion of provability, giving rise to claims that humans could beat formal systems in “knowing” theorems (see Davis (1990, 1993) for good discussions of such claims)."
• "From the time GL was formulated, researchers wondered whether it was adequate for formal theories like Peano Arithmetic (PA): does GL prove everything about the notion of provability that can be expressed in a propositional modal language and can be proved in Peano Arithmetic, or should more principles be added to GL?"
• "This will eventually allow Gödel to formalize the Liar paradox (with "provability" in place of "truth") by substituting into the formula which says, ˜the formula, whose code is"